Capability to manage the performance of a shared resources environment relies on the model estimation of all dynamics in the system. The main challenge is to capture the nonlinear characteristic which inherently exists in software system applications. Hammerstein-Wiener block structural model is widely regarded as a basis for description of nonlinear systems. This paper extends the existing wor...

The use of cubic splines, instead of polynomials, in representing static nonlinearities in block structured models is considered. A system identification algorithm for the Hammerstein structure, a static nonlinearity followed by a linear filter, is developed in which the static nonlinearity is represented by a cubic spline. The identification algorithm, based on a separable least squares Levenb...

In this paper a novel class of nonlinear Hammerstein adaptive filters, consisting of a flexible memory-less function followed by a linear combiner, is presented. The nonlinear function involved in the adaptation process is based on a uniform cubic spline function that can be properly modified during learning. The spline control points are adaptively changed by using gradient-based techniques. T...

This paper examines the use of a so-called “generalised Hammerstein–Wiener” model structure that is formed as the concatenation of an arbitrary number of Hammerstein systems. The latter are taken here to be memoryless nonlinearities followed by linear time invariant dynamics. Hammerstein, Wiener, Hammerstein–Wiener and Wiener–Hammerstein models are all special cases of this structure. The param...

This paper examines the use of a so-called “generalised Hammerstein–Wiener” model structure that is formed as the concatenation of an arbitrary number of Hammerstein systems. The latter are taken here to be memoryless non-linearities followed by linear time invariant dynamics. Hammerstein, Wiener, Hammerstein–Wiener and Wiener–Hammerstein models are all special cases of this structure. The para...

In this paper, we analyse the iterated collocation method for Hammerstein equations with smooth and weakly singular kernels. The paper expands the study which began in [14] concerning the superconvergence of the iterated Galerkin method for Hammerstein equations. We obtain in this paper a similar superconvergence result for the iterated collocation method for Hammerstein equations. We also disc...

Two existing Hammerstein-Wiener identification algorithms and a third novel Hammerstein-Wiener identification algorithm are considered for application to the magnetospheric system. A modified subspace algorithm that allows missing data points is described and used for identifying periodically switching Hammerstein-Wiener models, to capture the periodically time-varying nature of the system. The...

Introduction: Block-oriented structures are useful to model a nonlinear system. Applications range from RF amplifiers over chemical processes to physiological systems [1]. A block-oriented model consists of two types of blocks: Linear Time Invariant (LTI) and static nonlinear blocks. The most simple block-oriented model structures are the Wiener (a LTI block followed by a static nonlinear block...

In this chapter, we survey recent results on the numerical solutions of the Hammerstein equations. Hammerstein equations arise naturally in connection with the Laplace equation with a certain class of nonlinear boundary conditions. The Hammerstein equations with smooth as well as weakly singular kernels will be treated.